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    Subject

    Quantitative Aptitude

    Topic

    Time and Work

    Ana is thrice as efficient as Bill and is, therefore, able to finish a piece of work 10 days earlier than Bill. In how many days Ana and Bill will finish it together.

    ক)
    \(3\frac{1}{2}\) days
    খ)
    \(3\frac{4}{5}\) days
    গ)
    \(3\frac{3}{4}\) days
    ঘ)
    \(3\frac{7}{8}\) days
    ঙ)
    \(3\frac{5}{8}\) days

    Explanation

    Assume that the whole work is W units. Efficiency of Bill = B units/day Efficiency of Ana = 3B units/day Time taken by Bill to finish the work alone =  WB  days= \;\frac{W}{B}\;days Time taken by Ana to finish the work alone =  W3B  days= \;\frac{W}{{3B}}\;days According to the question, Ana can finish the work 10 days earlier than Bill. ⇒WB−W3B=10⇒WB=15\begin{array}{l} \Rightarrow \frac{W}{B} - \frac{W}{{3B}} = 10\\ \Rightarrow \frac{W}{B} = 15 \end{array} When they work together their combined efficiency is (B + 3B) = 4B units/day Time required to finish it together =  W4B=154=334days= \;\frac{W}{{4B}} = \frac{{15}}{4} = 3\frac{3}{4}days          [Using WB=15\frac{W}{B} = 15 days ]

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